How many ways are there to place 4 distinct gifts to 3 identical boxes?

Total ways to distribute 4 distinct balls into 3 boxes = 3*1 + 6*4 + 3*6 + 3*6 = 63.

How many ways can you distribute identical balls among identical boxes?

In total, there are 7 ways to group the balls. The “identical objects into identical bins” problem is closely related to the problem of partitioning an integer. Many of the same problem-solving strategies will be used.

How many ways can we distribute 5 distinct balls in 3 identical boxes if each box should have at least one ball?

We have to distribute 5 distinct balls into 3 identical boxes. Thus, n = 5 and k = 3. Therefore, there are a total of 41 possibilities.

How many ways can 6 different balls be distributed 3 boxes?

Ways of distributing 6 identical balls to 3 identical boxes: 4,1,1; 3,2,1; 2,2,2. Thus, there are 3 ways.

How many ways are there to distribute 6 identical balls in 3 different bags empty bags are allowed )?

As it is saying that no bin is empty, means every bin must have atleast one ball. After, putting one ball in each I am left with three balls. So left 3 balls can be put in C(5,2). But, the answer is 540.

How many ways are there to distribute 6 identical balls in 3 different bags empty bags are allowed?

How many ways are there to put 4 balls into 4 boxes where the balls are identical and the boxes are also identical?

Thus in total the balls can be divided in 15 ways in the four indistinguishable boxes.

How many ways are there to distribute 5 identical chocolates among 3 kids such that every kid gets at least 1 chocolate?

Therefore total ways is 150.

What is the number of ways distributing 5 identical balls into 3 boxes so that no box remains empty?

2 ways
So, there are only 2 ways to put 5 identical balls in 3 identical boxes such that no box is empty.

Can 5 different balls be distributed among three boxes?

Now, having 9 cases for each of those cases you can go on three different paths for the third ball, so the overall number of times becomes 9×3=27. Continuing like that till the 5th ball you get 3×3×3×3×3=35 different scenarios for the positions of the balls.

How many ways are there to put N identical balls into M numbered boxes?

* Now, every ball can be placed in boxes in three different ways. Hence, the total no. of ways of placing the rest 5 balls is 3*3*3*3*3=243.

How many ways can two balls be in the same box?

B)if the remaining two balls are in different boxes then simply there are six ways as (AB,C,D and AB,D,C are same as boxes are identical) hence no. Of ways = 6 4. One ball each in two boxes with two balls in one box which is same as above cases

What is the distribution of 4 balls into 3 boxes?

Distribution of 4 balls into 3 boxes, permitting 0 objects in some boxes, allows groupings of the 4 balls as follows: 4,0,0; 3,1,0; 2,2,0; 2,1,1. Given sets of balls can be arranged in the boxes respectively in a number of ways as follows: (4,0,0)-> (3!/2!)=3; (3,1,0)->3!=6; (2,2,0)->3!/2!=3; (2,1,1)->3!/2!=3.

What is the Bell number of the boxes?

Bell Number (B) is defined as the sum of all the values in the row corresponding to ’n’ upto ‘r’. If we consider that ALL the Boxes Should have Balls, the Solution is 6. If we consider that Boxes Can be left Empty, then the Solution is 14.